The Annals of Statistics最新文献_第10页

Optimal change-point estimation in time series 时间序列中最优变点估计

The Annals of Statistics Pub Date : 2021-08-01 DOI: 10.1214/20-aos2039

N. Chan, Wai Leong Ng, C. Yau, Haihan Yu

引用次数: 0

Charles Stein and invariance: Beginning with the Hunt–Stein theorem 查尔斯·斯坦与不变性:从亨特-斯坦定理开始

The Annals of Statistics Pub Date : 2021-08-01 DOI: 10.1214/21-aos2075

M. L. Eaton, E. George

{"title":"Charles Stein and invariance: Beginning with the Hunt–Stein theorem","authors":"M. L. Eaton, E. George","doi":"10.1214/21-aos2075","DOIUrl":"https://doi.org/10.1214/21-aos2075","url":null,"abstract":"When statistical decision theory was emerging as a promising new paradigm, Charles Stein was to play a major role in the development of minimax theory for invariant statistical problems. In some of his earliest work with Gil Hunt, he set out to prove that, in problems where invariant procedures have constant risk, any best invariant test would be minimax among all tests. Although finding it not quite true in general, this led to the legendary Hunt–Stein theorem, which established the result under restrictive conditions on the underlying group of transformations. In decision problems invariant under such suitable groups, an overall minimax test was guaranteed to reside within the class of invariant procedures where it would typically be much easier to find. But when it did not seem possible to establish this result for invariance under the full linear group, he instead turned to prove its impossibility with counterexamples such as the nonminimaxity of the usual sample covariance estimator where the full linear group was just too big for the Hunt–Stein theorem to apply. Further explorations of invariance such as the sometimes problematic inference under a fiducial distribution, or the characterization of a best invariant procedure as a formal Bayes procedure under a right Haar prior, are further examples of the far reaching influence of Stein’s contributions to invariance theory.","PeriodicalId":22375,"journal":{"name":"The Annals of Statistics","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86639897","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Correction note: “Statistical inference for the mean outcome under a possibly nonunique optimal treatment rule” 更正说明:“在可能非唯一的最佳处理规则下平均结果的统计推断”

The Annals of Statistics Pub Date : 2021-08-01 DOI: 10.1214/20-aos2031

Alexander Luedtke, Aurélien F. Bibaut, M. J. Laan

引用次数: 0

On Charles Stein’s contributions to (in)admissibility 论查尔斯·斯坦对可采性的贡献

The Annals of Statistics Pub Date : 2021-08-01 DOI: 10.1214/21-aos2108

W. Strawderman

引用次数: 0

Editorial: Memorial issue for Charles Stein 社论:纪念查尔斯·斯坦

The Annals of Statistics Pub Date : 2021-08-01 DOI: 10.1214/21-aos2110

R. Samworth, Ming Yuan

引用次数: 0

Monitoring for a change point in a sequence of distributions 监视一系列发行版中的变更点

The Annals of Statistics Pub Date : 2021-08-01 DOI: 10.1214/20-aos2036

Lajos Horváth, P. Kokoszka, Shixuan Wang

引用次数: 2

Stein 1956: Efficient nonparametric testing and estimation Stein 1956:有效的非参数检验和估计

The Annals of Statistics Pub Date : 2021-08-01 DOI: 10.1214/21-aos2056

A. Vaart, J. Wellner

引用次数: 0

Refined Cramér-type moderate deviation theorems for general self-normalized sums with applications to dependent random variables and winsorized mean 改进的一般自归一化和的cram<s:1>型中等偏差定理及其在相关随机变量和温化均值上的应用

The Annals of Statistics Pub Date : 2021-07-28 DOI: 10.1214/21-aos2122

Lan Gao, Q. Shao, Jiasheng Shi

引用次数: 2

Rate-optimal robust estimation of high-dimensional vector autoregressive models 高维向量自回归模型的速率最优鲁棒估计

The Annals of Statistics Pub Date : 2021-07-23 DOI: 10.1214/23-aos2278

Di Wang, R. Tsay

{"title":"Rate-optimal robust estimation of high-dimensional vector autoregressive models","authors":"Di Wang, R. Tsay","doi":"10.1214/23-aos2278","DOIUrl":"https://doi.org/10.1214/23-aos2278","url":null,"abstract":"High-dimensional time series data appear in many scientific areas in the current data-rich environment. Analysis of such data poses new challenges to data analysts because of not only the complicated dynamic dependence between the series, but also the existence of aberrant observations, such as missing values, contaminated observations, and heavy-tailed distributions. For high-dimensional vector autoregressive (VAR) models, we introduce a unified estimation procedure that is robust to model misspecification, heavy-tailed noise contamination, and conditional heteroscedasticity. The proposed methodology enjoys both statistical optimality and computational efficiency, and can handle many popular high-dimensional models, such as sparse, reduced-rank, banded, and network-structured VAR models. With proper regularization and data truncation, the estimation convergence rates are shown to be almost optimal in the minimax sense under a bounded $(2+2epsilon)$-th moment condition. When $epsilongeq1$, the rates of convergence match those obtained under the sub-Gaussian assumption. Consistency of the proposed estimators is also established for some $epsilonin(0,1)$, with minimax optimal convergence rates associated with $epsilon$. The efficacy of the proposed estimation methods is demonstrated by simulation and a U.S. macroeconomic example.","PeriodicalId":22375,"journal":{"name":"The Annals of Statistics","volume":"70 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83769165","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 11

The completion of covariance kernels 协方差核的完成

The Annals of Statistics Pub Date : 2021-07-15 DOI: 10.1214/22-aos2228

Kartik G. Waghmare, V. Panaretos

{"title":"The completion of covariance kernels","authors":"Kartik G. Waghmare, V. Panaretos","doi":"10.1214/22-aos2228","DOIUrl":"https://doi.org/10.1214/22-aos2228","url":null,"abstract":": We consider the problem of positive-semideﬁnite continuation: extending a partially spec- iﬁed covariance kernel from a subdomain Ω of a rectangular domain I × I to a covariance kernel on the entire domain I × I . For a broad class of domains Ω called serrated domains , we are able to present a complete theory. Namely, we demonstrate that a canonical completion always exists and can be explicitly constructed. We characterise all possible completions as suitable perturbations of the canonical completion, and determine necessary and suﬃcient conditions for a unique completion to exist. We interpret the canonical completion via the graphical model structure it induces on the associated Gaussian process. Furthermore, we show how the estimation of the canonical completion reduces to the solution of a system of linear statistical inverse problems in the space of Hilbert-Schmidt operators, and derive rates of convergence. We conclude by providing extensions of our theory to more general forms of domains, and by demonstrating how our results can be used to construct covariance estimators from sample path fragments of the associated stochastic process. Our results are illustrated numerically by way of a simulation study and a real example.","PeriodicalId":22375,"journal":{"name":"The Annals of Statistics","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82635870","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2